Calculus and Pre-calculus classes Next Year (2015-2016)

So next year I am going to flip both my Pre-calculus and Calculus class. For those of you that don't know that means for homework students watch videos and take notes as they are watching. Then in class they work in small groups on problems similar to those in the video. I then have the students present the problem that they solve. I will be using a similar structure or plan as I did when I flipped Pre-calculus in China.

Final: 20%
Presentations: 20%
Tests: 20%
Quizzes: 15%
Journal Entries/Notebooks: 15%
Homework: 10%

The presentations category will include their graded presentations using the rubrics I have used in the past. However before each presentation I will have students fill out a presentation outline. I will collect and grade the outlines as well. I came up with this outline last year in China. I was doing presentations with my grade 10 students in Pre-calculus and their English teacher was working on presentations. So I talked to my colleague which happened to my principal. He was having students fill out an outline before each presentation. It seemed very helpful for ESL/ELL learners about how to structure their presentation. It was also the structure I wanted my math presentations to follow. So I took the outline and I adjusted to fit my math presentations. It gave them something to work on once they were done solving their problem. It seemed to make students put more thought into their introduction and conclusion. It would have helped to have at the beginning of the year because I think it outlined and explained the structure I was looking for. Those first few presentations of my grade 10 students were not very good. I mean they were learning and it was the first time being in an English class, so it was not surprising. I just think it would have helped model and explain what I was looking for better. However I can start this year off using them and making students fill them out before the presentation. I also encourage students to bring them when they present, so they can refer to the outline as they are presenting.

The Journal Entry and Notebooks will include a few things. There will be content related journal entries that will be completed at the end of each unit. I have entries for each unit of Calculus and used them in China. They were fantastic and this is the rubric I used. When I taught 9th grade Honors math I had students answer a few journal entries. I covered some Pre-Calculus content so I think I can pull some prompts from the textbook they used which was Algebra & Trig: Graphs and Models, 5th edition, Bittinger, Beecher, Ellenbogen, and Penna. They had discussion or collaboration questions in the mid-chapter review and in the chapter review. They made good writing prompts. I also went to a talk at the NCTM conference that looked at supporting ESL/ELL students. After the talk I asked about writing prompts and if the speaker knew of resources that had good writing prompts. The speaker suggested Algebra Out Loud and Pre-Algebra Out Loud by Pat Mower. I have not checked these out yet, but I might.

As I wrote in my last post I will have students write about math in more general terms. They can relate math to different parts of their life and hopefully see math in a different way. I will grade these more simply and quickly. The key is just get the students thinking in a new way, writing, and using their English. Hopefully the way I have it set up will ensure that everyone gets a high score on these types of entries to improve the grade in this category. 

I will also be checking their notebooks at the end of each unit. I will check that they have the syllabus, vocab sheets, all of their notes, worksheets, previous journal entries, some presentation outlines and rubrics, previous quizzes, and previous tests. 

I am thinking about scoring it in this way:

5 points: missing one or two items
4 points: missing three or four items
3 points: missing five or six items
1 point: missing seven or more items

subtract a half point if not easy to find things. I will require the sections and will emphasize keeping things organized in the sections. Therefore I expect the notes and worksheets to be in the right order. They are numbered so they just need to stay in the right ordering. 

I am not grading the items just checking that they have all of them in their notebooks. I am planning on using 3 ring binders. They would have the syllabus and vocab sheets in beginning. Then it would be divided into the following categories: Notes, Worksheets, Journal Entries, Presentations, Quizzes/Tests.

I am planning on keeping a notebook for each class that would be the model and would have all the solutions in it. So completed vocab sheets, completed notes, completed worksheets, and answer keys to tests and quizzes. 

Homework category will include graded notes, worksheets, and vocab sheets. 

I will collect the notes handout once students are done presenting. I will grade them. I got pretty good and fast grading them when I taught in China. I looked that they filled in each part and each example then it was 5 out of 5. If they didn't fill out one or two things it was a 4 out of 5. If they left a lot of it blank then it was a 3 out of 5. That was pretty much it. However if students who went above in beyond like added things to the notes that were not required or showed that they highlighted key terms or content. So of my students turned in extremely neat, organized, and colorful notes that showed they put a lot of thought into the content. I gave them extra credit which means they got 6 out of 5. 

The worksheets are the problems students work on in class and the problems they present. I will tell students they have to finish the problems that were not presented as homework. I am thinking the first day of a section will be students solving the assigned problem, preparing the presentation and filling out the presentation outline, and then getting through some of the presentations. I don't think I can get through all of them in one day. So the next day will be the remaining presentations and then with whatever time is left they can finish the worksheet. I am thinking to minimize my grading I will pick 5 problems to grade that cover most of the worksheet and most of the objectives. I won't grade the problems that were presented. Then award points as following:

5 points: 1 problem wrong
4 points : 2 or 3 problems wrong
3 points: 4 problems wrong
1 point: 5 problems wrong

subtract half a point if they did not fill in the problems that were not presented on or did not complete entire worksheet. 

I think I will try having students keep vocab sheets. I have some great vocab sheets from an AP workshop that includes all the major theorems and concepts that come up the most often on the AP test. I think I will give time to review before each test to fill these out. I think I will encourage students to check these each night and fill them out as we go through the unit, but I don't want to require it and give them too much homework. So I usually give time in class to review before the exam and then I will have students fill those out. I will tell them which words they need to have done before the exam. Then I will check them in class while students are working in small groups working on review problems. I am thinking about how to grade them and want to do it fast. However I know the AP test looks for key things on the test and I want the vocab sheets to include everything that the AP test requires, but I don't want to spend forever grading them. I could make each one worth two points and if a word is missing something key in the definition or something is incorrect in the definition then subtract one point. 

I don't have vocab cards for Pre-calculus. However when I taught it in China I made digital ones use the grading software we had. I also gave online vocab quizzes to test them over the vocab. I also had fill in the blank questions that tested students over the definitions of the vocab words that I put on every test. So I have some of the vocab picked out and defined. So I will have to generate the vocab and definitions for some of the units as I go along.  

The school is a boarding school. So I will have to check how much access to the internet the students have. If it is a problem I have an easy solution. I had to find a way around using the internet when teaching in China since it was a boarding school with little access to internet, but also because general internet problems of China. I have digital copies of all the videos that I can download and copy over to a student's USB stick. In China I would download and copy the video onto the computer that was in the classroom. The students were then responsible to get a copy for themselves and to watch them. I wonder though if students will have enough access to a laptop or computer to watch the videos. I will have to ask my supervisors and the students.

Journal Entries that Challenge Students to See Math in a New Light

So I haven't posted in a while, but it was mainly because I had not been inspired at my previous jobs. However next year I will be teaching Pre-Calculus and AP Calculus AB at  an International school. I taught internationally for three years and learned to embed English into my curriculum to develop my ESL learners. I loved teaching in that environment and I found that I excelled at finding ways to embed English into my curriculum. I almost do it out of habit and it is hard to pick out all the ways I embed English. This idea of working on not only the content, but the language of mathematics has continually inspired me and pushed me to be more creative. The school seems to support innovative teaching and looks for teachers who find ways to embed English into their classroom. So I believe I will find my inspiration and get back to working on my passion.

Anyways last night I could not sleep and kept thinking about what I wanted to do for next year. I came up with some great ideas. I would to record them and share them so I don't forget. With my calculus class almost two years ago I had students write journal entries after each unit which related to the content. This past year I had my 9th grade honor students also write journal entries. I saw some amazing results. Many students demonstrated a very deep understanding of concepts through writing. One of my 9th graders wrote a beautiful piece that read just like any English assignment, was structured like an essay, and included three different mathematical perspectives or justifications. I know it challenged students that were not used to being challenged or challenged in this way.   I have often debated or thought of how to include writing pieces that were not about content. I thought about having students write about their feelings or attitudes towards math, so that I can understand students struggles in general. I would also hope that through these writings I could change students attitudes about math since many arrive to my classroom hating math or thinking they are bad at math. Although I didn't know how well students would receive such prompts. I personally have contemplated why math is so amazing, beautiful, and interesting to me. I want to open my students to that kind of thinking. So I want to try having students write about how math relates to some other concept that students may not have thought about in hopes to change their attitude or view of math. This is my idea for how to start the year.

I want to do a think, pair, share where students think about what is math. Many of my teachers in grad school had us do this. I think to the point that we got sick of it, but hey it is still cool to see the results. I did this with my Chinese students and I found it fun. I would generate a list for each class then combine the lists and enter the words in on wordle. This will show the words that came up more often as bigger. I am thinking that the next day I would show them and give them a copy of what was generated. I would then have students write what they think makes a good mathematician? I would encourage them to look back to what defines math, so they think about what skills you would need. I think this will get them in a mindset of what they need to do in my class (and beyond my class) to succeed.

However after the what is math discussion I want to lead it to another discussion. I want students to think about if math is a language. I have taken several Education classes that focused on teaching ESL students. I often was one of the few math teachers in the course. I believe you have to be creative in finding ways to embed English into math because you have to make sure students get practice on language of math as well as the English of math. Some of my classmates did not think you needed English to succeed in math. So not everyone can see the English involved in math or see that math is a language. My high school math teacher once said that math is a universal language that we can use to barter or haggle when we travel to other countries. After teaching international students for three years I gained a very deep understanding of how it is a language. For example many of my students had to learn how to say natural log of x (ln x). In China they say the function as "loin". I taught them and corrected them when they said that. I did this so that if they were discussing or talking about a problem with someone in America they would be understood. Students also asked me how to read x^2 or x^3. I told them to say x squared or x cubed. These are common examples I came across and there are more. So I want my students to understand or see how it is a language. I went to a talk at the National Teachers Council of Mathematics (NCTM) conference that introduced activities or strategies to support ESL students in mathematics. One activity was sort of like mathematical telephone. One person had to read an equation while two people listened. The people listening had to write down the equation. You switched roles until everyone had a turn reading an equation. I found it difficult to do as a reader because I had a very complex equation the had a bunch of fractions and parentheses in it. So I had to make sure I was very clear about what went where. I want to try this with my students on the first day. I was thinking I could use equations or expressions that they already know. For example equations that will help them review or prepare for the new content. I thought this would be a nice ice breaker and help get their brains thinking of the math they already studied. I think it would also demonstrate how math is a language. I would have students discuss what they learned or how they felt after the activity. Through this discussion I would guide students to think about how math is a language. Then I would have students write whether math is a language and why they believe that.

I want to try to incorporate writing assignments and writing prompts like this one during the year. I am hoping I could alternate between content specific journal entries and more general entries about the field of math.  Below are a few ideas for writing prompts that I have. If you can think of more or have some resources I would greatly appreciate it. I am hoping I will get inspired by my colleagues, students, and friends as the year goes on though.

There was an article I read a while back of a study that proved that when people look at a beautiful math equation the same part of the brain lights up if that person was looking at a beautiful piece of art. I think I could give the students the article and then ask them to respond in their own words whether they think math is beautiful. They would have to support their answer with examples and could refer back to the article if they wished.

Then related to the concept of beauty and art that was mentioned in the last one. Have students explore and write about how math is related to art. There is a big push and some resources out there to change the field of  Science Technology Engineering and Math (STEM) to include Art. So instead of thinking about STEM you would think of STEAM. This is because with those fields you need to experiment, fail, and explore. That requires some creativity and ingenuity that often is learned through art. I am working for the Calculus Project right now which strives to help students of color succeed in math and to reach Calculus. Numbers show that students of color are under represented in Calculus and other upper level math courses. In Oregon where I student taught most of the students in my lower level course that went twice as slow as the standard course were on free and reduced lunch. So there are factors outside of academics that could impact a students success in math as well as in other subjects. So the program gives students a preview and head start of the next years material. The program also brings in speakers and takes students on field trips. Recently a company called DEILAB came and ran a team building activity. They talked about the students to motivate them to succeed. They explained how art, creativity, and innovation were related to STEM. I like how they pointed out the Da Vinci painted art and was also an inventor to show art and STEM go hand in hand. Afterwards students got to design a robot that would win. They did this with lego pieces and a motor. The robot had to be a certain height. Then they would turn on the motor and the robot would spin to hit the other robot with arms and other weapons. Students would design and use their creativity to build a robot. Then they test their design and if it failed they were taught to learn from their failure. They were encouraged to fail so they could improve their design. It was amazing seeing students creativity and determination to perfect their designs and ideas. So I would like to have students write about how math and art are related. They could discuss how math is used in music or art. However I think they could also write about how you need the creativity from art to succeed in math. There was a book I read for an Education class that showed how math was used in art and in nature for kids. I think I could let students use that as a resource for the writing. As well as find a good article that explains how math is used in music.

I thought about how I would grade these. I would put these in the journal entry category of the grade. I would hope that these pieces would raise their grade in the journal entry category. I have a high expectation for the content entries and make getting a high grade on the assignment hard. So I would hope these more open and creative entries would be easier and raise grades. I was thinking of a rubric that would be fast and easy to use on these. So I am not spending forever grading these. I think these are the elements I would look for:

1. Answers question fully/Answers all parts of question
2. Includes math examples
3. Includes other non-math examples (art, music, or other topic that is discussed in prompt)
4. Connects/compares math examples and non-math examples
5. Organized/clear and neat

I think I would give them a check or a check minus in each category. A check would be two points and a check minus would be one point. So it would be a ten point assignment that they could get at least 5 points on. As long as they include all the pieces then they would get full points. However if they use unclear examples or their connections are unclear then they would lose points in the last category. So I see students losing points in the last category or the first.